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—In acoustic echo cancellation (AEC) applications, where the acoustic echo paths are extremely long, the adaptive filter works most likely in an under-modeling situation. Most of the adaptive algorithms for AEC were derived assuming an exact modeling scenario, so that they do not take into account the under-modeling noise. In this letter, a variable… (More)

—The performance of the recursive least-squares (RLS) algorithm is governed by the forgetting factor. This parameter leads to a compromise between 1) the tracking capabilities and 2) the misadjustment and stability. In this letter, a variable forgetting factor RLS (VFF-RLS) algorithm is proposed for system identification. In general, the output of the… (More)

—In this letter, we show that the normalized least-mean-square (NLMS) algorithm and the affine projection algorithm (APA) can be decomposed as the sum of two orthogonal vectors. One of these vectors is derived from an 2-norm optimization problem while the other one is simply a good initialization vector. By replacing this optimization with the basis… (More)

—Proportionate-type normalized least-mean-square algorithms were developed in the context of echo cancellation. In order to further increase the convergence rate and tracking, the " proportionate " idea was applied to the affine projection algorithm (APA) in a straightforward manner. The objective of this letter is twofold. First, a general framework for… (More)

—The adaptive algorithms used for acoustic echo cancellation (AEC) have to provide 1) high convergence rates and good tracking capabilities, since the acoustic environments imply very long and time-variant echo paths, and 2) low misadjustment and robustness against background noise variations and double-talk. In this context, the affine projection algorithm… (More)

The proportionate normalized least-mean-square (PNLMS) algorithm was developed in the context of network echo cancellation. It has been proven to be efficient when the echo path is sparse, which is not always the case in real-world echo cancellation. The improved PNLMS (IPNLMS) algorithm is less sensitive to the sparseness character of the echo path. This… (More)

—The Kalman filter is a very interesting signal processing tool, which is widely used in many practical applications. In this paper, we study the Kalman filter in the context of echo cancellation. The contribution of this work is threefold. First, we derive a different form of the Kalman filter by considering, at each iteration, a block of time samples… (More)

Proportionate-type affine projection algorithms were developed in the context of echo cancellation, as a generalization of the proportionate-type normalized least-mean-square algorithms. A matrix inversion is required within the affine projection algorithm (APA). In the case of proportionate-type APAs, the update of the matrix to be inverted is very… (More)